# Difference Amplifier Using Op-Amp | Subtractor Using Op-Amp

A difference amplifier is a circuit in which the output voltage is proportional to the difference between the input voltages.

Difference amplifier using op-amp can be obtained by connecting voltages to both input terminals of op-amp.

Difference amplifier is also known as Differential amplifier or Subtractor (with few changes).

## Circuit Diagram

In difference amplifier one of the Input V1 is given to non-inverting terminal and the other input V2 to the inverting terminal of op-amp.

Following circuit diagram shows the difference amplifier using op-amp. The feedback resistor Rf is connected from output to input. ## Derivation for Output Voltage

As one source is applied to each input terminal, let’s use Superposition Theorem to calculate output voltage.

To obtain output Vo, we determine output VO’ due to Input V1 alone and Vo” due to Input V2 alone.

Assume V1 to be short circuited i.e. connected to ground.

The difference amplifier circuit then reduced to an inverting amplifier with output VO’’ due to V2 alone as shown in following figure. This is an inverting amplifier hence output voltage is given by, …(1)

Where, -Rf/Ri is the gain of inverting amplifier.

Now, assume V2 to be short circuited i.e. connected to ground.

The difference amplifier circuit then reduced to a non-inverting amplifier with output VO’ due to V1 alone as shown in following figure. By potential divider rule, voltage at the point A, …(2)

For a non–inverting op-amp the output voltage is given by, …(3)

From equation (2) and (3), …(4)

If R2=R1,R3=Rf,

Therefore equation (4) becomes,  …(5)

By Superposition theorem, Putting values of and in above expression [from equation (1) and (5)] we get, …(6)

Thus, output is proportional to difference between the inputs. Hence this circuit is known as difference amplifier.

## Subtractor

In the equation (6) if we substitute if Rf=R1=R then the expression of output voltage is given by, Thus, the difference amplifier gets transformed into a subtractor.

The subtractor circuit is shown in the following figure. It is same as difference amplifier except values of resistances. Note that, all the resistances are having same value (R). The gain of subtractor is 1.

## Formula

The output voltage of a difference amplifier is given by, .

Where,

Rf is feedback resistance.

R1 is input resistance (at inverting terminal).

V1 is the voltage applied at non-inverting terminal and

V2 is the voltage applied at inverting terminal.

If Rf=R1 then This is the output voltage expression for subtractor.